A sampling clock of a certain sampling frequency is needed for performing a sampling process for converting an analog signal into a digital signal. Generally, to convert an analog video signal into a digital video signal, a sampling clock in synchronization with a horizontal sync signal or a vertical sync signal is used.
According to Nyquist's theorem, when a sampling frequency is fsc, if the highest frequency component of an input signal is lower than fsc/2, information on waveforms of the input signal is not lost, that is, original waveforms of the input signal can be reproduced with perfection. However, this holds only when the input signal and the sampling clock are in an optimum condition in terms of their phases.
The reason for this will be explained with reference to FIGS. 8 and 9 below. FIG. 8 shows an input signal Ain of a constant frequency and an output signal (a sample) Aout obtained by sampling the input signal Ain by use of a sampling clock Aclk which has a frequency that is twice that of the input signal Ain, and is in an optimum phase relation with the input signal Ain. When the input signal Ain is sampled by use of this optimum sampling clock Aclk, difference between the highest level and the lowest level, that is, the amplitude of a resultant output signal representing its AC component is at its maximum as apparent from FIG. 8.
FIG. 9 shows the same input signal Ain and an output signal Bout obtained by sampling this same input signal Ain by use of a sampling clock Bclk which is 180° (π radians) out of phase with the sampling clock Aclk. When the input signal Ain is sampled by use of this sampling clock Bclk that is most distant from the optimum sampling clock Aclk, the amplitude (AC component) of a resultant output signal is at its minimum (zero) as apparent form FIG. 9. As described above, if the same input signal is sampled, the amplitude of a resultant output signal varies depending on a phase of a sampling clock. It is also well known that the variation range of the amplitude of an output signal obtained by sampling an input signal depends on the frequency of a sampling clock as shown in FIG. 10.
In the graph of FIG. 10, the horizontal axis represents a frequency of an input signal, and the vertical axis represents an amplitude (its maximum value is normalized to 1) of an output signal obtained by sampling the input signal by use of a sampling clock of a frequency fsc. The curve Cmax represents amplitudes of the output signal when the input signal and the sampling clock are in the optimum phase relation, the curve Cmin represents amplitudes of the output signal when they are most distant from the optimum phase relation, and the curve Cave represents average amplitudes of the output signal. From this graph, it is apparent that the amplitude of the output signal varies widely depending on the phase of the sampling clock not only when the frequency fsc of the sampling clock is twice that of the input signal, but also when it is three or four times that of the input signal.